Find the critical values $\chi^{2} L_{\text {and }} \chi_{R}^{2}$ for the given confidence level $c$ and sample size $n$. \[ \mathrm{c}=0.95, \mathrm{n}=30 \] $\chi_{\mathrm{L}}^{2}=16.047$ (Round to three decimal places as needed) \[ \chi_{\mathrm{R}}^{2}=\square \text { (Round to three decimal places as needed.) } \]

Step 1 ：We are given a confidence level of 0.95 and a sample size of 30. We are asked to find the critical values for a chi-square distribution.

Step 2 ：The chi-square distribution is defined for positive values and is skewed to the right. It has a single parameter, the degrees of freedom, which is equal to the sample size minus 1 for a sample variance.

Step 3 ：The critical values for a confidence level c are the values of the random variable such that the probability of the variable being less than or equal to those values equals \((1-c)/2\) and \((1+c)/2\) respectively. For a confidence level of 0.95, these probabilities are 0.025 and 0.975.

Step 4 ：We already have the left critical value \(\chi_{L}^{2}=16.047\). We need to find the right critical value \(\chi_{R}^{2}\).

Step 5 ：Given that the degrees of freedom is 29 (sample size minus 1), we can use the chi-square percent point function (PPF) to find the right critical value. The PPF gives the value of the random variable such that the probability of the variable being less than or equal to that value equals the given probability.

Step 6 ：Using the PPF, we find that the right critical value \(\chi_{R}^{2}\) is approximately 45.722.

Step 7 ：Final Answer: The right critical value for the given confidence level and sample size is \(\boxed{45.722}\).